A lifting engine of that type for example is known from U.S. Pat. No. 3,489,374, which is a typical design representative for many similar designs in the literature.
All these designs have the disadvantage in common, that the part of the thrust, which stems from the underpressure acting on the convexly curved inlet fairing is small, whereas the major part of the thrust is generated within the narrow diameter of the axial fan (propeller) as the difference of total pressures between suction side and pressure side. This fact causes a small ratio of "lifting force F to engine power P", shortly designated as F/P and therefore a more high specific fuel consumption. Furthermore there is the disadvantage of less positional stability during hovering flight due to small amount of stabilizing aerodynamic underpressure forces acting on big radii from the fan center line on the inlet fairing.
The different designs of inlet fairings in the state of the art show endeavors to keep that disadvantage small, but there was never an attempt to involve the geometry of the fan blades.